| cor_lagr_tri {mcgf} | R Documentation |
Calculate Lagrangian correlation of the triangular form
Description
Calculate Lagrangian correlation of the triangular form
Usage
cor_lagr_tri(v1, v2, k = 2, h1, h2, u)
Arguments
v1 |
Prevailing wind, u-component. |
v2 |
Prevailing wind, v-component. |
k |
Scale parameter of |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
Details
The Lagrangian correlation function of the triangular form with parameters
\boldsymbol v = (v_1, v_2)^\top\in\mathbb{R}^2 has the form
C(\mathbf{h}, u)=\left(1-\dfrac{1}{k\|\boldsymbol v\|}
\left|\dfrac{\mathbf{h}^\top\boldsymbol v}{\|\boldsymbol v\|}-
u\|\boldsymbol v\|\right|\right)_+,
where \|\cdot\| is the Euclidean distance, x_+=\max(x,0),
\mathbf{h} = (\mathrm{h}_1, \mathrm{h}_2)^\top\in\mathbb{R}^2,
and k > 0 is the scale parameter controlling the magnitude of
asymmetry in correlation.
Value
Correlations of the same dimension as h1.
See Also
Other correlation functions:
cor_cauchy(),
cor_exp(),
cor_fs(),
cor_lagr_askey(),
cor_lagr_exp(),
cor_sep(),
cor_stat(),
cor_stat_rs()
Examples
h1 <- matrix(c(0, -5, 5, 0), nrow = 2)
h2 <- matrix(c(0, -8, 8, 0), nrow = 2)
u <- matrix(0.1, nrow = 2, ncol = 2)
cor_lagr_tri(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u)
h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3))
cor_lagr_tri(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)